gftool.fermi_fct_d1
- gftool.fermi_fct_d1(eps, beta)[source]
Return the 1st derivative of the Fermi function.
\[f'(ϵ) = -β\exp(βϵ)/{[\exp(βϵ)+1]}^2 = -βf(ϵ)[1-f(ϵ)]\]- Parameters:
- epsfloat or float np.ndarray
The energy at which the Fermi function is evaluated.
- betafloat
The inverse temperature \(beta = 1/k_B T\).
- Returns:
- float or float np.ndarray
The Fermi function, same type as eps.
See also
Examples
>>> eps = np.linspace(-15, 15, num=501) >>> fermi_d1 = gt.fermi_fct_d1(eps, beta=1.0)
>>> import matplotlib.pyplot as plt >>> _ = plt.plot(eps, fermi_d1) >>> _ = plt.xlabel(r"$\epsilon/\beta$") >>> _ = plt.axvline(0, color='black', linewidth=0.8) >>> _ = plt.xlim(left=eps.min(), right=eps.max()) >>> _ = plt.ylim(top=0) >>> plt.show()